The present invention relates to a new and distinct variety of plum tree, herein after referred to by the cultivar name ‘Suplumthirtyfive.’ The new variety ‘Suplumthirtyfive’ originated by hybridization, being first hybridized by Bruce Mowrey and selected by David Cain. The new variety was first evaluated by David Cain and Terry Bacon near Wasco, Calif. in Kern County.